/* From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
   by RH Landau, MJ Paez, and CC Bordeianu 
   Copyright Wiley-VCH, 2007.
   Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
   MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
   Support by National Science Foundation                              
   */
// pspaceJamaEigen.java: solve Lippmann-Schwinger eq for bound states

import Jama.*;  
import java.io.*;
    
public class pspaceJamaEigen  {
	
  public static void main(String[] argv) throws IOException,
                                  FileNotFoundException  {   
    Gauss gauss = new Gauss();
    double u = .5;
    double eps = 1.0*Math.pow(10,-8);
    int b = 2, i, j, g, temp3 = 0, size = 128;
    double temp = 0, temp2, test = 0, min = 0.0, max = 200.0;
    double lambda = -1.0;
    Matrix H = new Matrix(size, size);
    Matrix Psi = new Matrix(size, size);

    PrintWriter q = new PrintWriter ( 
		                      new FileOutputStream("pspace.dat"), true);
    Matrix ev = new Matrix(size,1);
    Matrix a1 = new Matrix(size,1);
    Matrix a2 = new Matrix(size,1);
    Matrix ground = new Matrix(size,1);
    double[] w = new double[size];
    double[] k = new double[size];
    double[] y = new double[size];
    double[] z = new double[size];
    double[] im = new double[size];
    double[][] VR = new double[size][size];
    gauss.gauss(size, 0, min, max, k, w);

   for( i=0; i<size; i++ )  {	      	   // Set up hamiltonian matrix
     for( j=0; j<size; j++ )  {
       VR[i][j] = (lambda*b*b/(2*u))*
         	  (Math.sin(k[i]*b)/(k[i]*b))*(Math.sin(k[j]*b)/(k[j]*b));
       if (i == j)  H.set(i,j, k[i]*k[i]/(2*u) 
				                     + (2/Math.PI)*VR[i][j]*k[j]*k[j]*w[j]);
       H.set(i,j,(2/Math.PI)*VR[i][j]*k[j]*k[j]*w[j]);
     }
   }
                                                        // E = eig(H)
   EigenvalueDecomposition E = new EigenvalueDecomposition(H);
   y = E.getRealEigenvalues();
   im = E.getImagEigenvalues();
   
   for ( i=0; i<size; i++ ) {
     System.out.println(y[i]);
     if ( y[i] <0 ) {
   	   if ( Math.abs(y[i]) > Math.abs(temp) ) {
   		   temp = y[i];
   		   temp3 = i;
   		}
   	}
   }
   Psi = E.getV();
   for(j=0; j<size; j++) {
    	for(i=0; i<size; i++) {
   	  	temp2 = Psi.get(i,j);
  		  ev.set(i,0,temp2);
  		}
  	  a1 = H.times(ev);
  	  a2 = ev.times(temp);	
  	  test = 0;
  	  for ( g=0;g<size;g++ ) test+=Math.abs(a1.get(g,0)-a2.get(g,0));
  		if ( test<eps ) {
  		  System.out.println("good");
  		  ground = ev;
  		  for ( g = 0; g<size; g++ ) q.println(ground.get(g,0) );
  		}
    }		
 }
}